Mathematics faculty/staff worksCopyright (c) 2022 SUNY Geneseo All rights reserved.
https://knightscholar.geneseo.edu/math-faculty
Recent documents in Mathematics faculty/staff worksen-usSun, 06 Mar 2022 01:41:47 PST3600Analysis of a Time-Delayed HIV/AIDS Epidemic Model with Education Campaigns
https://knightscholar.geneseo.edu/math-faculty/7
https://knightscholar.geneseo.edu/math-faculty/7Fri, 04 Mar 2022 13:20:12 PST
We consider a time-delayed HIV/AIDS epidemic model with education dissemination and study the asymptotic dynamics of solutions as well as the asymptotic behavior of the endemic equilibrium with respect to the amount of information disseminated about the disease. Under appropriate assumptions on the infection rates, we show that if the basic reproduction number is less than or equal to one, then the disease will be eradicated in the long run and any solution to the Cauchy problem converges to the unique disease-free equilibrium of the model. On the other hand, when the basic reproduction number is greater than one, we prove that the disease will be permanent but its impact on the population can be significantly minimized as the amount of education dissemination increases. In particular, under appropriate hypothesis on the model parameters, we establish that the size of the component of the infected population of the endemic equilibrium decreases linearly as a function of the amount of information disseminated. We also t our model to a set of data on HIV/AIDS in order to estimate the infection, effective response, and information rates of the disease. We then use these estimates to present numerical simulations to illustrate our theoretical findings.
]]>
Sedar Ngoma et al.Space-Efficient Prime Knot 7-Mosaics
https://knightscholar.geneseo.edu/math-faculty/6
https://knightscholar.geneseo.edu/math-faculty/6Fri, 04 Mar 2022 13:20:09 PST
The concepts of tile number and space-efficiency for knot mosaics were first explored by Heap and Knowles in 2018, where they determined the possible tile numbers and space-efficient layouts for every prime knot with mosaic number 6 or less. In this paper, we extend those results to prime knots with mosaic number 7. Specifically, we find the possible values for the number of non-blank tiles used in a space-efficient 7 7 mosaic of a prime knot are 27, 29, 31, 32, 34, 36, 37, 39, and 41. We also provide the possible layouts for the mosaics that lead to these values. Finally, we determine which prime knots can be placed within the first of these layouts, resulting in a list of knots with mosaic number 7 and tile number 27.
]]>
Aaron Heap et al.Surface Reconstruction from Constructive Solid Geometry for Interactive Visualization
https://knightscholar.geneseo.edu/math-faculty/5
https://knightscholar.geneseo.edu/math-faculty/5Tue, 02 Nov 2021 07:20:08 PDT
A method is presented for constructing a set of triangles that closely approximates the surface of a constructive solid geometry model. The method subdivides an initial triangulation of the model’s primitives into triangles that can be classified accurately as either on or off of the surface of the whole model, and then recombines these small triangles into larger ones that are still either entirely on or entirely off the surface. Subdivision and recombination can be done in a preprocessing step, allowing later rendering of the triangles on the surface (i.e., the triangles visible from outside the model) to proceed at interactive rates. Performance measurements confirm that this method achieves interactive rendering speeds. This approach has been used with good results in an interactive scientific visualization program.
]]>
Doug BaldwinIs Computer Science a Relevant Academic Discipline for the 21st Century
https://knightscholar.geneseo.edu/math-faculty/4
https://knightscholar.geneseo.edu/math-faculty/4Tue, 02 Nov 2021 07:20:06 PDT
The current view of computing as technology overlooks the discipline’s theoretical and scientific foundations in computer science, weakening the entire computing enterprise.
]]>
Doug BaldwinExistence of traveling wave solutions of a deterministic vector-host epidemic model with direct transmission
https://knightscholar.geneseo.edu/math-faculty/3
https://knightscholar.geneseo.edu/math-faculty/3Mon, 01 Nov 2021 08:38:13 PDT
We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less than one, we show that there is no nontrivial traveling wave solution. On the other hand, when the basic reproductive number is greater than one, we prove that there is a minimum wave speed c such that the system has a traveling wave solution with speed c connecting both equilibrium points for any c ≥ c. Moreover, under suitable assumption on the diffusion rates, we show that there is no traveling wave solution with speed less than c . We conclude with numerical simulations to illustrate our findings. The numerical experiments supports the validity of our theoretical results.
]]>
Dawit Denu et al.Adjustable Algorithmic Tool for Assessing the Effectiveness of Maternal Respiratory Syncytial Virus (RSV) Vaccination on Infant Mortality in Developing Countries
https://knightscholar.geneseo.edu/math-faculty/2
https://knightscholar.geneseo.edu/math-faculty/2Tue, 19 Oct 2021 12:36:57 PDT
Acute lower respiratory infection (ALRI) due to RSV is a common cause of global infant mortality, with most cases occurring in developing countries. Using data aggregated from priority countries as designated by the United States Agency for International Development’s (USAID) Maternal Child Health and Nutrition (MCHN) program, we created an adjustable algorithmic tool for visualizing the effectiveness of candidate maternal RSV vaccination on infant mortality. Country-specific estimates for disease burden and case fatality rates were computed based on established data. Country-specific RSV-ALRI incidence rates for infants 0-5 months were scaled based on the reported incidence rates for children 0-59 months. Using in-hospital mortality rates and predetermined “inflation factor,” we estimated the mortality of infants aged 0-5 months. Given implementation of a candidate maternal vaccination program, estimated reduction in infant RSV-ALRI incidence and mortality rates were calculated. User input is used to determine the coverage of the program and the efficacy of the vaccine. Using the generated algorithm, the overall reduction in infant mortality varied considerably depending on vaccine efficacy and distribution. Given a potential efficacy of 70% and a maternal distribution rate of 50% in every USAID MCHN priority country, annual RSV-ALRI-related infant mortality is estimated to be reduced by 14,862 cases. The absolute country-specific reduction is dependent on the number of live births; countries with the highest birth rates had the greatest impact on annual mortality reduction. The adjustable algorithm provides a standardized analytical tool in the evaluation of candidate maternal RSV vaccines. Ultimately, it can be used to guide public health initiatives, research funding, and policy implementation concerning the effectiveness of potential maternal RSV vaccination on reducing infant mortality.
]]>
Rachel Cevigney et al.Introduction to Zoom for Teaching
https://knightscholar.geneseo.edu/math-faculty/1
https://knightscholar.geneseo.edu/math-faculty/1Mon, 02 Nov 2020 10:25:07 PST
This document presents an introduction to the basic tools of teaching with Zoom.
]]>
Sedar Ngoma